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Kurzweil-Stieltjes integral and its generalizations
Konopka, Filip ; Slavík, Antonín (advisor) ; Tvrdý, Milan (referee)
The thesis deals with the HKSp α integral, which is generalization of the HKS integral, its properties and the concepts of ordinary oscillation and p-oscillation, which are needed for the construction of the integral. This integral is non-absolutely convergent and more general than the Lebesgue integral. This thesis is based on recent results in the theory of integrals and its goal is to introduce this integral to a wide readership interested in mathematical analysis. 1
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Nonabsolute convergence of Newton integral
Konopka, Filip ; Spurný, Jiří (advisor) ; Vlasák, Václav (referee)
In this thesis, we look for sufficient conditions for non-absolute convergence of Newton integral. Importantly we analyse how the oscillation of the sine function influences the con- vergence of the integral. We are dealing with the convergence of integrals based on the limits of the antiderivative, which does not need to convergence in the Lebesgue sense. 1
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Kurzweil-Stieltjes integral and its generalizations
Konopka, Filip ; Slavík, Antonín (advisor) ; Mošna, František (referee)
The thesis deals with the HKSp α integral, which is generalization of the HKS integral, its properties and the concepts of ordinary oscillation and p-oscillation, which are needed for the construction of the integral. This integral is non-absolutely convergent and more general than the Lebesgue integral. This thesis is based on recent results in the theory of integrals and its goal is to introduce this integral to a wide readership interested in mathematical analysis. 1
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Nonabsolute convergence of Newton integral
Konopka, Filip ; Spurný, Jiří (advisor) ; Zelený, Miroslav (referee)
In this thesis we search for sufficient and necessary conditions for non abso- lute convergence of Newton integral of function of the form sin φ(x) x . Importantly we analyse how the oscilation of the sine function influences the convergence of the integral. We are dealing with continous non-decreasing functions such that limx→∞ φ(x) = ∞. We proved that bilipschitz of φ is not sufficient. Nevertheless, we proved several theorems about sufficient conditions for the convergence of the integral. 1
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Nonabsolute convergence of Newton integral
Konopka, Filip ; Spurný, Jiří (advisor) ; Vlasák, Václav (referee)
In this thesis, we look for sufficient conditions for non-absolute convergence of Newton integral. Importantly we analyse how the oscillation of the sine function influences the con- vergence of the integral. We are dealing with the convergence of integrals based on the limits of the antiderivative, which does not need to convergence in the Lebesgue sense. 1
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